Though the overall sales in the app stores (Apple and Google) are still increasing, they are increasing much more slowly than the number of available apps, and developers are able to charge less today than in the past for each app, resulting in a situation where the vast majority of apps just aren't worth building as products in themselves. Fewer and fewer people are buying their first phone, and first phone buyers are the main buyers of apps. People on their third phone don't do much shopping for new and interesting apps. They just use what they've been using--the apps that came with the phone plus a handful of other standards from, say, Google, Facebook, and Twitter--and beyond that they don't care.
It's getting to the point where the only reason to develop a new commercial app (as opposed to a personal project) will be as a component in a business that sells things other than apps. If you are trying to build a business selling apps (including in-app purchases of upgrades and add-ons), your chances of success are falling fast.
So, apps are not only "killing the Web", they are in that same sense killing themselves.
What's really dying here is just the potential for most people to make a fortune building websites or phone apps as competition drives it toward ordinary compensation for ordinary work.